Winning Strategy Templates for Stochastic Parity Games towards Permissive and Resilient Control

2024-09-13

International Colloquium on Theoretical Aspects of Computing

AI Summary

This work addresses the limited adaptability of controllers in stochastic games under dynamic constraint changes and environmental disturbances. Methodologically, it extends permissiveness-based strategy templates—previously confined to deterministic games—to the stochastic setting, yielding generalizable and dynamically reconfigurable stochastic winning strategy templates. The approach integrates stochastic game modeling, fixed-point computation, symbolic state-space traversal, and parity game solving to devise provably correct template construction and instantiation algorithms for five classes of objectives: safety, reachability, Büchi, co-Büchi, and parity. Key contributions include (i) support for infinite strategy representations and runtime elastic reconfiguration, and (ii) novel mechanisms for template extraction and comparative analysis. Experimental evaluation demonstrates significant improvements in robustness and adaptability of cyber-physical system controllers operating in dynamic environments.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Stochastic games play an important role for many purposes such as the control of cyber-physical systems (CPS), where the controller and the environment are modeled as players. Conventional algorithms typically solve the game for a single winning strategy in order to develop a controller. However, in applications such as CPS control, permissive controllers are crucial as they allow the controlled system to adapt if additional constraints need to be imposed and also remain resilient to system changes at runtime. In this work, we generalize the concept of permissive winning strategy templates, introduced by Anand et al. at TACAS and CAV 2023 for deterministic games, to encompass stochastic games. These templates represent an infinite number of winning strategies and can adapt strategies to system changes efficiently. We focus on five key winning objectives -- safety, reachability, B""uchi, co-B""uchi, and parity -- and present algorithms to construct templates for each objective. In addition, we propose a novel method to extract a winning strategy from a template and provide discussions on template comparison.

Problem

• Generalizing strategy templates from deterministic to stochastic games
• Capturing infinite winning strategies for system adaptation
• Addressing almost-sure and positive winning criteria across objectives

Innovation

• Generalizing strategy templates to stochastic games
• Capturing infinite winning strategies for adaptation
• Providing algorithms for template construction and extraction